Evaluate. $243^{^{\scriptsize\dfrac{7}{10}}}\cdot 243^{^{\scriptsize\dfrac{1}{10}}}=$
$\begin{aligned} 243^{^{\scriptsize\dfrac{7}{10}}}\cdot 243^{^{\scriptsize\dfrac{1}{10}}}&=243^{^{\scriptsize\dfrac{7}{10}+\dfrac{1}{10}}} \\\\ &=243^{^{\scriptsize\dfrac{8}{10}}} \\\\ &=243^{^{\scriptsize\dfrac45}} \\\\ &=\left(\sqrt[5]{243}\right)^4 \\\\ &=3^4 \\\\ &=81 \end{aligned}$ In conclusion, $243^{^{\scriptsize\dfrac{7}{10}}}\cdot 243^{^{\scriptsize\dfrac{1}{10}}}=81$